What is laplacetransform 2cos(t-pi/6) ?

The answer to laplacetransform 2cos(t-pi/6) is (sqrt(3)s+1)/(s^2+1)

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laplacetransform 2cos(t-pi/6)

laplace transform

2 cos (t - \frac{π}{6})

\frac{3 s + 1}{s ^{2} + 1}

Solution steps

L {2 cos (t - \frac{π}{6})}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 2 L {cos (t - \frac{π}{6})}

L {cos (t - \frac{π}{6})} : \frac{3 s + 1}{2 ( s ^{2} + 1 )}

= 2 \cdot \frac{3 s + 1}{2 ( s ^{2} + 1 )}

Refine

2 \frac{3 s + 1}{2 ( s ^{2} + 1 )} : \frac{3 s + 1}{s ^{2} + 1}

= \frac{3 s + 1}{s ^{2} + 1}

\int_{0}^{\infty} e^{- y} d y

\int 7 x + 8 y^{2} d x

\int \frac{1}{( x - 5 ) ^{2} ( x + 3 )} d x

x \frac{d y}{d x} + y = 4 x + 1

f (x) = \frac{3}{x}, at x = 3

What is laplacetransform 2cos(t-pi/6) ?
The answer to laplacetransform 2cos(t-pi/6) is (sqrt(3)s+1)/(s^2+1)